一道简单的向量题

题目

一道简单的向量题
已知A(-3,0),B(0,√3),O为坐标原点,点C在第二象限,且∠AOC=60°,向量OC=λ向量OA+向量OB,则实数λ的值是多少?

答案

OC = λOA + OB
= λ(-3,0) + (0,√3)
= (-3λ,√3)
OA .OC = (-3,0).(-3λ,√3)
= 9λ ----(1)
also
OA .OC = |OA||OC| cos∠AOC
= 3.[√(9λ^2 + 3 )] .1/2 --(2)
(1)=(2)
6λ = √(9λ^2 + 3 )
36λ^2 = 9λ^2 + 3
λ^2 = 1/9
λ = 1/3 or -1/3 (rejected)
As C is 第二象限,=> λ = 1/3